Most real and engineered systems, including transportation infrastructure, are embedded in space and interact with one another in a variety of ways. To study such systems, a novel multi-layer spatially embedded random network model is proposed. In the development of this model, concepts from spatial statistics and graph theory are used to map complex systems with interdependent subsystems to a simplified and condensed mathematical representation. The developed model combines Markov marked point processes for vertex creation, which accounts for spatial distribution, layer assignment, and clustering effects of the vertices, and a hybrid connection model for the edge creation. To test the capabilities of, and gain insights with respect to, a real-world network, the model was used to model a complex infrastructure system, comprised of the power grid and road network of Switzerland. It was found that, even with very simple assumptions, topological properties could be estimated reasonably well.